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  {
   "source": [
    "# Identifying Effect using ID Algorithm\n",
    "\n",
    "This is a tutorial notebook for using the ID Algorithm in the causal identification step of causal inference.\n",
    "\n",
    "Link to paper: https://ftp.cs.ucla.edu/pub/stat_ser/shpitser-thesis.pdf\n",
    "The pseudo code has been provided on Pg 40.\n",
    "        "
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from dowhy import CausalModel\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from IPython.display import Image, display\n"
   ]
  },
  {
   "source": [
    "## Examples\n",
    "\n",
    "The following sections show the working of the ID Algorithm on multiple test cases. In the graphs, **T** denotes the treatment variable, **Y** denotes the outcome variable and the **Xs** are additional variables."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "## Case 1\n",
    "\n",
    "This example exhibits the performance of the algorithm on the simplest possible graph."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Graph:\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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\n",
      "text/plain": "<IPython.core.display.Image object>"
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\nResult for identification using ID Algorithm:\nPredictor: P(Y|T)\n"
     ]
    }
   ],
   "source": [
    "# Random data\n",
    "treatment = \"T\"\n",
    "outcome = \"Y\"\n",
    "causal_graph = \"digraph{T->Y;}\"\n",
    "columns = list(treatment) + list(outcome)\n",
    "df = pd.DataFrame(columns=columns)\n",
    "\n",
    "# Causal Model Initialization\n",
    "causal_model = CausalModel(df, treatment, outcome, graph=causal_graph)\n",
    "\n",
    "# View graph\n",
    "causal_model.view_model()\n",
    "from IPython.display import Image, display\n",
    "print(\"Graph:\")\n",
    "display(Image(filename=\"causal_model.png\"))\n",
    "\n",
    "# Causal Identification using the ID Algorithm\n",
    "identified_estimand = causal_model.identify_effect(method_name=\"id-algorithm\")\n",
    "print(\"\\nResult for identification using ID Algorithm:\")\n",
    "print(identified_estimand)\n"
   ]
  },
  {
   "source": [
    "## Case 2\n",
    "\n",
    "This example exhibits the performance of the algorithm on a cyclic graph. This example demonstrates that a directed acyclic graph (DAG) is needed for the ID algorithm."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Graph:\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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\n",
      "text/plain": "<IPython.core.display.Image object>"
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Identification Failed: The graph must be a directed acyclic graph (DAG).\n"
     ]
    }
   ],
   "source": [
    "# Random data\n",
    "treatment = \"T\"\n",
    "outcome = \"Y\"\n",
    "causal_graph = \"digraph{T->Y; Y->T;}\"\n",
    "columns = list(treatment) + list(outcome)\n",
    "df = pd.DataFrame(columns=columns)\n",
    "\n",
    "# Causal Model Initialization\n",
    "causal_model = CausalModel(df, treatment, outcome, graph=causal_graph)\n",
    "\n",
    "# View graph\n",
    "causal_model.view_model()\n",
    "from IPython.display import Image, display\n",
    "print(\"Graph:\")\n",
    "display(Image(filename=\"causal_model.png\"))\n",
    "\n",
    "try:\n",
    "    # Causal Identification using the ID Algorithm\n",
    "    identified_estimand = causal_model.identify_effect(method_name=\"id-algorithm\")\n",
    "    print(\"\\nResult for identification using ID Algorithm:\")\n",
    "    print(identified_estimand)\n",
    "except:\n",
    "    print(\"Identification Failed: The graph must be a directed acyclic graph (DAG).\")\n"
   ]
  },
  {
   "source": [
    "## Case 3\n",
    "\n",
    "This example exhibits the performance of the algorithm in the presence of a mediator variable(**X1**)."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Graph:\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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UUlJCnKqVxs1HKOdeT09v6tSp+MPDhw9TbQEAFR0+fBi/8qlnz55Dhgyh2gKduZ9mz56NL1+6dCk/P59GIwDQI5fLd+7ciT+cM2cOPkum8ujkftSoUfgkgSiKEosAgG1///13QUEBtiwSiRYuXEijETq5F4vFK1aswB/GxsbCZSiAM7/++iu+PG7cOA8PDxqN0Jzj8v333yfeUG7Hjh302gGAkrS0tMuXL+MPIyMj6bVDM/cWFhbz5s3DH/70009wQhNw4Ntvv0VRFFt2d3cfN24cvXboz2m8evVqfX19bLmqqmr79u20mwJAGampqcRb1X7zzTf0J+Wm+sUK0Ycffoi3Y2lpWVlZqUprAHRt+PDheN68vLykUintplSaw/6rr74yMDDAlmtqar766itVWgOgC0eOHLlx4wb+MDo6mtJEUWQq/gmuWrUKb0osFqempqrYIACKJBIJ8TJCf39/mUymSoOq5r6urs7BwQEvKCAgQJVPHwA69MUXX+AZE4lEycnJKjaoau5RFD1w4ADxA+SHH35QvU0AcMnJycQuzYIFC1RvU4T+c1ZIlZ7S8OHD8XFCBgYGqamplC52BKAzTU1Nfn5++FgYCwuLnJwcSlNEdYiBe7OJRKJ9+/bhX2O1trYuWLAAZhkBjPjiiy+IA8C2bt2qeugRROXjWty2bduIzS5btoyploFgxcfHE0M1efJkplpmLPdyuZx0jeMff/zBVONAgHJzc/H5mhAEsbGxKSsrY6pxxnKPouirV69sbW3xQo2NjR88eMBg+0A4GhoaiIeIYrH4/PnzDLbP5L2XnZycjhw5gh96NzY2vvPOOzDnAqBKJpPNmzfv4cOH+E++/vprGhcTdoXBvyHMunXriO0PGjSooaGB8a0ALbZy5UpihEaNGsX4l0LM514mk02fPp1Yd1hYWHt7O+MbAlrpp59+IobHzc2NjXFfzOceRdGmpqbAwEBi9TNmzIDogzfat28f8aJBKyur3NxcNjbESu5RFK2srCRNibFgwQIVx1QA7XbgwAHiuGJ9ff2EhASWtsVW7lEUzcnJsbGxIUZ/+fLlcrmcvS0CzfXnn38SByPo6OgcOXKEvc2xmHsURR88eGBlZUWM/nvvvdfW1sbqRoHGiYuL09XVxUMiEol27drF6hbZzT2Konfu3CF++4AgyKRJk5qbm9neLtAUW7duJU0EsnnzZrY3ynruURS9efOmmZkZ6cxUTU0NB5sG6kwmk33++efEYIhEIg5Cj3KTexRF79+/T+rr9+nTh6VDdaARmpubiROQYX16trs3OI5yj6JoTk6Os7Mz8fe0srJKTEzkrACgPkpKSgYPHkwMg76+fnx8PGcFcJd7FEWfP3/u7e1N+m23b9/OZQ2Ad7dv33ZyciLGwMzM7NKlS1zWwGnuURStr69/5513kH+bM2cOjGUQiF27duHTz2CcnJzS09M5LoPr3KMo2tbW9sEHH5Ci37dv38ePH3NfDOBMTU3Nu+++S3rfhwwZUlpayn0xPOQe88svv5D+7rt167Z161b4YksrXb9+nXjfb8z8+fObmpp4qYe33KMompqaqnh7ltGjR798+ZLHqgCz2traFOe6MTAwiImJ4bEqPnOPomhFRQXxhlkYKyur2NhY2PFrgZSUFMUZBnr16nX//n1+C+M59yiKyuXymJgYfN413LBhw3JycviuDtAkkUiioqIUpzQLDw+vrq7muzo1yD3mwYMHijuGbt26ff/99y0tLXxXB6g5fvw46bsaBEEsLS1ZHWpGibrkHkXR5ubmzz//XHEP0bt377/++ovv6oBSHjx4MHLkSETB2LFj1eqwTY1yj7l//76fn5/iCzdq1Ci4Sl2dVVZWLlu2THG3ZWNjo4Yza6hd7lEUbW9vj4mJMTExIb2CYrE4PDw8Pz+f7wLBvzQ0NGzcuNHc3FxxbxUeHl5RUcF3gR1Qx9xjXrx4ER4ervhS6unpLVu27NWrV3wXCNCmpqYff/wRv58xkZ+f340bN/gusFPqm3vMnTt3Orw7qb6+fkRERF5eHt8FClR9fX1MTIyjo6PiW9O9e/eYmBg1nxZb3XOPoqhMJtuzZ4/i+QEEQXR1defOnZuVlcV3jQJSUVHx1VdfWVhYKL4dRkZGUVFRtbW1fNf4ZhqQe0xra+uuXbvs7OwUX24EQYKDg48ePQpTNrAqIyNj6dKlRkZGHXY+ly5dWlxczHeNytKY3GPq6+vXrl1LumYX17t3782bN6vD1yLapK2tLT4+fujQoR2+5np6egsXLiwoKOC7TGo0LPeYhoaGmJiYDns+CIIYGBiEh4efOXNGzbuY6i8nJycqKqqzz1gDA4OIiIgnT57wXSYdGpl7TEtLy2+//dbF7apdXV2jo6Ph2JeqqqqqnTt3dng6AWNpabl69ery8nK+K6VPg3OPkcvlV65cCQ8P7+Ludn379o2OjoYT/12rra2Ni4sLCwsjjQ8n8vT0jImJkUgkfBerKo3PPS4/P//jjz/urOuPIIhIJBo8ePD3338P3/sSFRcX79q1a+LEiYpDA3H6+vozZsy4fv0638UyhoH7W6mV1tbWU6dO7du37+rVq3K5vLOn9ezZMywsbOLEiSEhIfgdioRDJpOlpaVdunTpzJkzaWlpXWTAx8fn/fffnzt3Lmk6DE2nbbnHFRUVHThw4MiRI48fP+7iafr6+m+//XZoaGhoaGhAQICenh5nFXIvOzv72rVrCQkJiYmJtbW1XTzT3t5+xowZERERAQEBnJXHJa3NPe7x48fHjh2Lj4/Pzc3t+pl6enoDBgwIDg4eOnTo8OHDifdu0VBNTU3p6elpaWlJSUmJiYmVlZVdP9/KymrixInh4eETJkwgTtynfbQ/97isrKyzZ8+eOXPm/v37XXSBcG5ubn5+fr7/IE19oZ7q6uoyCR49eiSVSt+4lpub26RJkyZNmjRs2DDtjjtOQLnHlZWVnTt37sKFC4mJidXV1Uqu1b17d29vby8vL09PT09PTy8vLxcXly6OBdkml8tLSkry8/Pz8vJyc3Nzc3Pz8vIKCwuVXN3AwCAwMHDcuHGTJk3q168fq6WqISHmHieTyTIyMhISEhISEpKSkpqamiitLhKJ7O3tXV1dXVxcXFxcnJycrK2tbW1t7ezsbGxsrK2tuzghqAwURSsrK6uqqiorK8vLyysqKioqKgoLCwsLC4uKil69etXe3k6pQR0dHT8/P+xgJjg4uMMRBwIh6NwTSaXSjIyMlJSUlJSUpKSkly9fqt6moaGhsbGxubm5mZmZsbFxt27dEAQxNjYm/T3I5fK6ujoEQdrb2yUSSW1tbWNjo0QikUgkqtdgYWERGBgYGBgYFBQUEBBAmptasCD3HSspKcnIyMB6yRkZGdj4E76LUoqdnR12QIIdnLi7uxNvIgIwkHulNDQ05P4D608/e/aspaWF36p0dHRcXFw8PDy8vb2xo46+fft2NpwGEEHu6SsrKyv6R2FhYWVlZVlZWeU/lDllpAwLCwvsgMHGxsbBwcHR0dHFxaVnz57YEYVATr8wDnLPChRFa2tra2trJRIJ1lmvqalBEKS+vl4mk928efPQoUPYM/38/JYtW4YgiIWFhUgkMjU1NTY2NjExMTc3NzU1NTc3V/HgGHQI9hasEIlElpaWlpaWHf6vXC7Hc9+rV6+lS5dyWBpAEASBIx4gRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IES6fBegJaqrq2tra5V8clVVFb7c2NhYUFCg5IoGBgZOTk6UiwMKRCiK8l2DNjh+/Hh4eDjbW1m6dOmuXbvY3ooQQO6Z0dLSYmdnV19fz+pWrl27NnLkSFY3IRDQv2eGoaHhtGnTWN2Eo6PjsGHDWN2EcEDuGTNnzhy229fR0WF1E8IB/RzGyGQyJyen8vJyltq/f/++v78/S40LDezvGaOjo8PeoW2fPn0g9AyC3DOJva7O3LlzWWpZmKCfwyQURd3c3J4/f854y9nZ2d7e3ow3K1iwv2eSSCSaPXs24836+/tD6JkFuWcYG10dts8UCRD0c5jXv3//R48eMdWaWCwuLCx0dnZmqkGAwP6eDczunocNGwahZxzknnlz584ViURMtQadHDZAP4cVQUFBKSkpqrejp6dXWlravXt31ZsCRLC/ZwVTO+nx48dD6NkAuWfFrFmzdHUZuLYBOjksgdyzwtbWVvUBw0ZGRpMmTWKkHkACuWeL6rvqKVOmmJiYMFIMIIHcs+Xdd9/t1q2bKi1AJ4c9kHu2mJmZTZgwgfbqlpaW48aNY7AeQAS5Z5EqO+zw8HB9fX0GiwFEcP6eRS0tLfb29nV1dTTWvX79+ogRI5iuCPwv2N+zyNDQcOrUqTRWdHR0DAkJYbwegIPcs4teVwcupWUb9HPYRe+iW7iUlm2wv2cXjYtu4VJaDkDuWUe1qwOX0nIA+jmso3rRbW5urqenJ6slAdjfs47SRbf+/v4Qeg5A7rmgfFcHxiZwA/o5HFHmolu4lJYzsL/niDI7criUljOQe44oc9EtdHI4A/0c7nR90S1cSssl2N9zp+vdOVxKyyXIPXe6vugWOjlcgtxzx9bWdtSoUR3+l7Gx8eTJkzmuR8gg95zqbKc+ZcoUY2NjjosRMsg9p6ZPn97hRbfQyeEY5J5THV50a2lpOXbsWF7qESzIPdcUd+0zZ86ES2k5BufvuaZ40W1iYuLw4cN5LEmAGJjLDpBIJJLy8vLa2tqamhqJRNLY2CiRSGpraxEEqa2tRVG0R48eeO5NTU3Pnz9/4cIFMzMzHR0dExMTY2NjExMTCwsLExMTc3NzW1tbOK/PONjf04GiaHFxcWFhYWFhYdE/ysvLy8vLq6qqmpubmd2crq6ujY2NtbW1vb29k5OTq6trz549e/To4eLi4urqCn0kGiD3b9bW1vbo0aPc3NycnJz8/Py8vLz8/HzGw02Prq5uz549PT09vby8PD09PT09Bw4caG5uzndd6g5y34HGxsb79+9nZGRkZmZmZmZmZ2e3t7fzXRQFvXv39v1HQECAnZ0d3xWpHcj9/yosLExKSkpJSUlOTs7KypJKpaq01q1bN2trazMzM2NjYzMzM3Nzc2NjY0NDQwRBjI2N9fX1i4uLDx48OHTo0ODgYBRFsd6/TCarr6+vq6vDDgkaGhoqKysbGhpU/NX69OkTGBgYGBgYHBzs4+MjFsNJPGHnvqKi4tq1awkJCQkJCVRvOqujo+Po6Ih1tV1cXFxcXBwdHW1sbGxtbW1tbd84jzF20e3Fixc9PDy6fmZra2tlZWVlZWV5eXlFRcWLFy/wI4rCwsKWlhZKZVtZWY0YMWL06NGhoaFv3LQWE1zuZTLZ3bt3z549e+HChaysLCV/fVNTUx8fH29vbw8PDw8PDy8vLzc3NxUPKI8fPz5jxgxVWkBRtKioCDvkyM3NzcvLe/jwofJz9fTo0WPcuHFhYWFjxowxMjJSpRKNI5TcNzY2Xrhw4dy5c+fPn6+srHzj862srAICAnx9fY5v04EAACAASURBVP38/Hx9ffv06aMp3YPS0tLMzEzs4OTevXuFhYVvXKVbt26jRo2aNGnS5MmTHRwcOCiSd1qe+5aWlosXL8bHx589e7axsbGLZ4pEIm9v78DAwKCgoMDAQC8vLwbvScijkpIS7KAlJSUlLS2tra2tiyeLxeJhw4bNmjVrxowZ1tbWnBXJPe3MPYqiiYmJ+/fvP3XqVH19fRfPdHV1Df2H1p/3aGxsvHXrFnY88+DBA7lc3tkzdXV1Q0NDIyIiOhtIp+m0LfcvX77cv3///v37CwoKOnuOnp7e8OHDw8LC3nnnHXd3dy7LUx9VVVWXL18+c+bMpUuXsLNJHbKwsJgzZ87ixYvfeustLstjHaoVZDLZ+fPnJ0yY0EUv3MzMbO7cufHx8dhgAYBpa2tLSEj45JNPXFxcusjJgAEDdu3a1djYyHe9zND43NfX1+/atatv376dvWGGhoZhYWFxcXESiYTvYtXd/fv3IyMjHR0du9h3REZGFhQU8F2pqjQ498XFxatWrTI1Ne3wHRKLxaGhoQcPHoS4UyWVShMSEubNm9dZz15HR+fdd9+9f/8+35XSp5G5LygoiIyM7OxdcXJyioqKevr0Kd9lary6urq4uLjRo0d3tvsPDg4+c+YM32XSoWG5f/r06bx58zq8F4hIJBozZsyZM2dkMhnfZWqb9PT0xYsXY+MsFAUFBV27do3vGqnRmNwXFxcvW7ZMT09P8XU3MTFZsWJFdnY23zVqucrKyg0bNvTo0aPD9I8ZM+bevXt816gsDch9XV3dF1980WGvpnv37mvWrKmqquK7RgFpa2uLjY319vbu8CN3+vTpT5484bvGN1Pr3Mtksr1793b4dZKzs/OWLVsaGhr4rlGgZDLZiRMnOjypr6+v/8UXX9TV1fFdY1fUN/e3bt0aNGiQ4stqY2OzZcuW5uZmvgsEKIqip06d8vHxUXyb7O3t9+3bJ5fL+S6wY+qY+9ra2sjISMVvoExMTKKiouBbJ3Ujk8mOHj3a4TffwcHBjx8/5rvADqhd7o8fP644JFBHR2fp0qUVFRV8Vwc61dbWtmXLFgsLC9J7Z2BgsHbt2tbWVr4L/Bc1yn1FRcX06dMV9xnDhw/PyMjguzqglIqKiqVLlyqeaO7Xr59afc+lLrk/d+6c4vGrvb39kSNH+C4NUJaRkREQEEB6N/X09NavXy+VSvmuDkXVIfcSieTDDz8kDXYXiURLliypqanhuzpAk1QqjYmJUbzeMjg4+NmzZ3xXx3fuc3JyFIeUubu7JyYm8lsYYERhYeE777xDen/Nzc3/+usvfgvjM/cnT55UnOklIiICzsprmbi4ONKOXyQSRUZGtrW18VUSP7lvb2+PjIxU7M3//fffvNQD2Jafnz9kyBDSOx4SElJWVsZLPTzkvqamZsyYMaSXYNy4cXCaUru1t7dHRUWRDuRcXV2xWS04xnXuCwoKSB16kUgUFRWlJof5gG1nz561tLQkBsDExOTs2bMcl8Fp7u/cuWNjY0P8nbt3737x4kUuawC8e/r0qa+vLzEGOjo6O3fu5LIG7nKfmJhoZmZG/G379OmTm5vLWQFAfUgkkqlTp5L6ulFRUZwVwFHuz507RxpIPHTo0MrKSm62DtSQXC6Pjo4mRT8yMpKboWxc5D4+Pp50vciiRYt4PIcF1MeuXbtIgxpWrFjBQfRZz/2pU6dIoV+5ciVcCghwp06dIl3BGBkZyfZG2c395cuXSb8Sl304oCkSEhJI82J89dVXrG6RxdzfuHGD1Kf/6aef2Nsc0Gi3bt0i3bl648aN7G2Ordw/ffqUdMpy3bp1LG0LaIeEhATijlIkEv3xxx8sbYuV3FdVVZGuvvnss8/Y2BDQMpcuXTIwMMBjo6+vz9IMJcznvqWlJSgoiBj65cuXM74VoK3i4+OJl5h2796djSnAmM/9smXLiKEfP358e3s741sBWmzjxo3ECPXv35/x+WgZzv3hw4eJFfv4+MBl4ICGFStWEIM0d+5cZttnMvePHj0iHpLb2NgUFRUx2D4Qjvb29hEjRhCjv3fvXgbbZ+y+D21tbYMHD87KysIeisXiCxcujB07lpHGgQCVl5cPGjSopKQEe2hkZJSRkcHUPRgZu1fZ2rVr8dAjCPLdd99B6IEq7Ozsjh8/jn/Z39TUtHDhQplMxkzrjHxq3Lt3T1dXF29zzJgxMBIBMOL7778nxnXTpk2MNMtAP6e9vX3QoEGPHj3CHpqbmz98+LCzWXMBoEQqlQ4dOvTu3bvYQwMDg4cPH6p+VzIG+jnbtm3DQ48gSExMDIQeMEVXVzcuLg7/Hre1tXXlypUMtKvi50VpaSnxapLx48cz8SkEOiWRSJYvX46/4Obm5nxXxIXNmzcTQ6v6TVZUzf38+fPxagwMDPLz81VskHuKVz90TUdHp8N2UlNTlWyB9jV1ycnJffr0ITYlkNy3tbURL8t2c3NraWlRpUGV+jnZ2dkHDx7EH65atUqwt4NlW3t7+9dffx0SEvL06VO+a+GBnp7etm3b8IfPnj3bu3evKg2qlPu1a9fi97x2dnb+z3/+o0proDOPHz8eMmTI+vXrGTuLp4FGjRr17rvv4g83bNjQ0tJCvznanxSPHj0ijh/67bffVPncUR/jx49XfJVo/HZ3797Fr6Dbs2cPvWLkcvnPP/9MHKJIIpB+DiYvL494ujwmJoZ2U/RzP3v2bLwCV1dXdZvgnLaioiLSvA8IgpiamlIac9Hc3Ozl5YWtO2HCBHqVvHjxYvjw4cQyZs6cOXLkSMHmHkXRefPm4b+7o6Mj7dTRzH1xcTHxqlna+zP1tHv3bsU967hx45Rv4bPPPsPWsrS0LC4uplFDbGws8c/P1tb2xIkTKIoSP+sFmPsnT54Qd/mHDx+m1w7N3H/11Vf4th0cHLRmZ49TnMkQQZB9+/Yps+6tW7fwHuChQ4dobL2hoYG43dmzZ+P3bBR47lEUnTlzJv7rBwYG0muETu5bWlpsbW3xbUdHR9Pbtjp78eKF4tztFhYWb9x5SyQSNzc37Pnvvvsuva3jubezszt58iTxvyD3t27dIr4C9G6jQif3J06cwLeqp6dH73Nc/e3YsUNxlz9p0qSu18IHjtva2tKeGAvL/Xvvvff69WvSf0HuURT19/fHX4H/+Z//odECndzPmjUL32p4eDiNFjSCXC4nHURiuui6XL16FZ/vl7SfpqSlpeXUqVMd/hfkHkXRXbt24a+AnZ0djQv6KOdeIpEQLy5R5d1VfwUFBaTJLRAE6d69e3l5ueKT6+rqXFxcsOfMnz+fpZIg9yiKVldX6+vr4y/C5cuXqbZA+Xurc+fONTY24i96h2e7tUavXr02bNhA+uHr16//53/+R/HJn376aVFREYIgzs7OW7du5aI+obK0tCSeeIiPj6fcBNU/lIULF+LrLliwgOrqGkcul4eEhCi+bseOHSM+7e+//8b/69KlS+zVA/t7zB9//IG/CM7OzlRXp5x74hjjo0ePUl1dEz158oQ08RuCILa2tvi5xerqakdHR+zny5YtY7UYyD2mqqqKOFwgJyeH0urU+jk5OTkvX77ElsVicYeHfdqnT58+69evJ/2woqICv0XXRx99hF0G2rt3b9KIWcCS7t27E28eceXKFUqrU8t9YmIivjxo0CBra2tKq2uujz/+ODAwkPTDw4cPnz179uTJk4cOHUIQRCwW79+/X/E4GLCE2MUnJlMZ1HKfkZGBL5OGjmg3sVgcGxtLmtsZQZAPP/wQnyfrk08+6fBIALCEmMD09HRK61LLPbH1QYMGUVpX03l6en733XekH5aWllZUVCAI4u3trdgXAqwifntVWFhYXV2t/LoUci+VSh8/fow/JN2aSwg+++yzgIAAxZ9j14AqfhoAVtna2jo4OGDLKIo+ePBA+XUp5L6goAAf6W9oaMjUDD4aREdHJzY2VnE0vJWVlQBfDXVA3PlmZ2crvyKF3GNfymB69epFHA4qHH379v32229JP6yoqFi1ahUv9Qgc8Wpj/EyjMijkntiukGcKWbhwIelWZAiC/P7775cvX+alHiEj5hByzy7svnSKP//ggw9I4+YB27jIfVVVFb5sb2+v/Ira5ODBgydPnuzwv4qKiv7f//t/HNcjcPhxLYIglZWVyq9IIfdNTU34sjC/nSkpKcG/o/3kk08GDx5MesLu3buvXbvGeV3CRcxhc3Oz8itSyD2xXSMjI+VX1BpLliypqalBEMTb23vDhg2xsbHE0bAIgqAoumTJEny8KmAbMYfE/fIb0dzfK47T0np79uy5cOECgiC6uroHDhwwNDTs16/fN998Q3ra8+fPv/zySz4KFCJi7intbhib/167vXjxAj9T+eWXX7711lv4suL31r/++uuNGzc4rQ9QRCH3xL8tSn0pTYei6OLFi7FzNQMHDiSev9fV1d23bx9xShXs+e+//z6lj11AD+1jTpq5F9Sbum3btuvXryMIoq+vf+DAAVLKBw4cqDhB4rNnz4hTrQCWEHNI6ZiTQu6JfXrhHLo9efJk9erV2HJ0dPSAAQMUn/PVV18p/vyXX35JTk5mvT5hI+aQrdzb2Njgy6WlpcqvqLlkMtmCBQuwnUpAQEBUVFSHT9PT04uNjSUN3JDL5YsWLVJp7lLwJvhd35B/5/ONKOSe9ndjmmvz5s0pKSkIghgaGsbFxSkOT8ANGjRI8a8iPz9f8YQPYBBxzBilMQQ0c0/cnrZ69OgRfkuI9evX4/O8dubbb7/t168f6YdbtmzB780EGEd77AzN3BcWFkqlUuXX1ThSqXTBggWtra0IgoSEhHzyySdvXEVfXz82Npb0mYD1drB2AOMKCgrwZbZy37t3b/zSipaWltzcXOXX1Tjff/89dnGZsbFxbGws8dL9LgwePPjzzz8n/TAnJ2fNmjWMVwiQf1/4qvhh2xVKsy/g39cgCPLHH39QWleDpKWl4QepO3bsoLQuceZ7nI6OTmpqKiO1wTwiOOJBrUgkqq6uVn5dat/X+vn54ctUr+TVFK2trfPnz8d6caNHj8YvG1eSoaHhvn37SJ8PMpls0aJFbW1tTBYqeMSdfc+ePS0tLZVfl1ruid/J37x5k9K6muLbb7/FLiM2MzPbt28fPs+r8gIDAxWPBx49erRu3TpmSgQIgiAIcTAI5VkOKH2y5OTk4CuKxeKKigqKH03qiNRz6EIX83o/fPiQ2uuOIGfPnu26MDs7O6pt4h4+fMj066R2iFnftm0bpXWp7e+9vLzwo2a5XI59ew8A916/fp2ZmYk/7PD+NF2gPB5z9OjR+DJxMlQAuHThwgXiPWQ9PT2prU/1w4U457K5uXlzczPVFgBQ3cSJE/EcLlmyhOrqlPf3YWFh+I2f6urqsEsxAOBSdXU1cSJY4i1llUQ590ZGRmFhYfjDP//8k2oLAKjo6NGj+ElhOzu7ESNGUG2BzvVWxD+vU6dOFRcX02gEANp27tyJL8+aNauL8YKdoZP7CRMm4POItLe3d3iXYwBYcvPmzaysLPzhggULaDRCJ/f6+vpLly7FH/72228w7gpwZtu2bfhycHAwvXm5aV5XvmzZMvxyu4qKiri4OHrtAEDJkydPTp06hT/86KOP6LVDM/cODg7ErznXr18Pg08AB9auXYsPgHd0dJw+fTq9dujPI/L111/jo6+Kiop+//132k0BoIzs7Gzi+cOoqCjSNf4UqPLdAfHG5U5OTg0NDaq0BkDXpk2bhufN2dlZle9MVZo36ttvv8V3+cXFxT/88IMqrQHQhYSEBOKMvP/5z39UucGMCEVRVapZvHhxbGwstmxgYPDw4UN3d3dVGgRAUXt7u6+vL35Hkz59+jx+/Jg0OSklqs4TuGHDBnNzc2y5tbUVny4YAAZt3bqVeBufmJgYVUKPIKr17zFbtmwhNrh3717V2wQAl5OTQ5yzbOzYsaq3qWo/B0EQqVTq5+f36NEj7KGZmdnDhw9dXFxUbBYABEGkUmlwcPC9e/ewh4aGhllZWar3pRmYD1lXV5c4W1h9ff3ixYvxsdEAqGLjxo146BEEWbduHTMHkKp/ZGBIE4OtXbuWqZaBYCUmJhJnXwwKCpJKpYy0zEA/ByOVSt9+++20tDTsoVgs/vvvv8ePH89I40CAysvLBw0ahE8WYmxsnJGRwdTZQsbu+4DdBQS/JEUul8+fP18g02gCxkml0lmzZhFnyNm+fTuTp8gZ+dTAHTlyhNh4v379amtrmd0EEILly5cTg/TBBx8w2z7DuUdRdMWKFcSKx40b197ezvhWgBYjffE/YMCApqYmZjfBfO5bWlqCg4OJdS9dupTxrQBt9eeffxLn6rKxsXn27BnjW2E+9yiKVlVVeXh4EKP/ySefsLEhoGUuXrxoYGCAx8bQ0DApKYmNDbGSexRFnz17Rrr/xJo1a1jaFtAOV69eJQ41E4lEhw4dYmlbbOUeRdFbt26Rbjm0ceNG9jYHNNqNGzdINyTcvHkze5tjMfcoil65coU0WDQqKorVLQJNdPXqVfwMOCY6OprVLbKbexRFL1y4QOyxIQiyYsUKmUzG9naBpjh58iQpIR9//DHbG2U99yiKHj16lHQ9WERERGtrKwebBmru119/Jc1+s3LlSrlczvZ2ucg9iqLnzp0jDiVFECQ4OFg7phEH9EilUsU7QHLWDeYo9yiK3rhxw8zMjPhLurm55eTkcFYAUB8SiWTKlCnEMIhEok2bNnFWAHe5R1E0NTWVdC8DS0vLc+fOcVkD4F1+fj7p9u56enq///47lzVwmnsURV+9ekW8SRb2hx4ZGQljGQTi9OnTFhYWxACYmpr+/fffHJfBde5RFK2rq1McnxwaGlpWVsZ9MYAzbW1tq1atIt0vrHfv3tnZ2dwXw0PuURRtb2//9NNPSS+Bra3tmTNneKkHsC03N5d4E1jMyJEj+Tq3wU/uMadOnSJ95CEIEhERAfNPaZm4uDjSd7FY57atrY2vkvjMPYqieXl5/fv3J0W/T58+169f57cwwIgXL14o9mktLS15/2DnOfcoijY2Nq5YsYLU5xGJRIsXL379+jXf1QGapFLpli1bSLt5BEFCQkKeP3/Od3VqkHvM+fPn8XtJ4Ozs7A4dOsTBt3eAWampqf7+/qR3U19ff8OGDUxdGK4idck9iqKVlZUd3kJ56NChaWlpfFcHlFJaWrp48WJ81lRcv3791OpNVKPcY/766y8nJyfSqyYWi99//3040anOWltbN23aRPpKHkEQAwOD7777Tt2GY6ld7lEUrauri4yMVLxZl7GxcVRUVE1NDd8Fgn+RyWRHjx51c3Pr8LOal9Pzb6SOucekpKQEBAQovpRWVlabNm1qbGzku0CAyuXyY8eOeXt7K75Njo6OcXFxantspr65R1FULpfv37/fwcFB8WW1t7fftGlTXV0d3zUKlFQqPXLkiK+vr+JbY2houHr1ajX/Ekatc49paGj4z3/+o3hGDEEQCwuLr7/+GsYzc6m1tXXv3r0dTuEkEolmzpxZUFDAd41vpgG5x5SWlq5cubLDWc+NjIyWLl2alZXFd41arqysbN26dY6OjopvAYIg77zzTnp6Ot81Kktjco95/vz5woULiXOFEo0cOfLEiRNqcoZYm9y7dy8iIoJ0NSBu+PDht27d4rtGajQs95gXL15ERkaSJmvAOTg4REVF5efn812mxqutrd21axdpFjCi4ODgq1ev8l0mHRqZe0xZWdmXX36J32WIRCQSDRs2bP/+/fX19XxXqmGkUunFixdnz57d2Y3TdHV1Z8+enZmZyXel9Glw7jHNzc1xcXE+Pj6d7ZMMDQ3DwsLi4uLU/AwD72Qy2a1btyIjIxUHjOAsLCwiIyNfvHjBd7Gq0vjcY+Ry+ZUrVyZPnqz4bRfO2Nh45syZhw4dqq6u5rteNdLa2nr58uWVK1d2dsCK8ff337dvnyq3jFUrjN33QU2UlJQcOHAgNjY2Pz+/s+fo6uqGhISEhYVNnDjR09OTy/LUR0VFxeXLl8+cOXPp0qX6+vrOnmZlZTVv3rzFixcPHDiQy/LYpm25x6Aoevv27f379588ebKmpqaLZzo7O4f+o+sdnhZoaGi4cePGtWvXEhISHj582MVbr6+vP2bMmIiIiKlTp3Z2GkejaWfucW1tbZcvX46Pjz99+nRDQ0PXT/bw8AgMDAwKCgoKCurbt6/ioEJN9PLly6SkpJSUlJSUlIyMDKlU2sWTdXV1R40aNWvWrGnTpllaWnJWJPe0PPe4lpaWS5cunT179ty5c+Xl5W98vpmZWUBAgK+vr6+vr5+fn6enZxdHDmqlqKgo8x/37t0rLi5+4ypGRkZjx44NCwubMmWKtbU1B0XyTii5x8nl8tTU1DNnzly4cOHBgwdK3m+0W7du/fr18/b29vLy8vT09PT0dHd3570DIJfLCwsL8/LycnJy8vLy8vLysrKyqqurlVzd1dV13LhxkydPHjVqFGk2O60nuNwTVVVVXb9+PSEh4dq1a0+ePKG0rlgsdnBw6Nmzp8s/nJycbGxsrK2t7e3tFYeh09bc3FxZWVleXl5RUVFeXl5UVFRYWFhUVFRUVPTy5cvW1lZKrdnY2IwcORI7nulw5LBACDr3RMXFxcnJycnJySkpKenp6e3t7aq0ZmBgYG1tbWpqamJiYmFhYWJiYmxsjA2tMzAwIH3T3NbW1tjYiC1IJJLa2lqJRNLY2NjQ0FBZWYn9F20ikcjT0xM7bgkMDOzbty/pUmZhgtx3oLm5OT09PSMjA+slP3r0iOpulUdisbhPnz7YYYmvr+/gwYO7d+/Od1FqB3L/ZlKpNCcnJycnJzc3Nzc3F+tJq7gbZoqenl6vXr28vb2xo46+ffv6+PiQ7qEAFEHu6UBRtLS0lNjPfvHiRWVlZVlZmeo9E0X6+vo2NjY2NjYODg5OTk49evTAjyt69OhBurcAUAbknnlNTU2VlZVVVVV1dXWNjY0SiaShoaGurk4ulzc1NbW2tmZkZFy+fBl7soeHx7Rp03R0dLBDYTMzM+xgwMzMzNzc3MzMzM7OTnFWOaAiyD0PfvvtN/x+3NOnTz9x4gS/9QiQNnwlCQBVkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IESQeyBEkHsgRJB7IEQiFEX5rkEbxMXFLVy4kO2tzJ079+DBg2xvRQhgf8+MadOmGRoasr2VWbNmsb0JgYDcM8PMzCwsLIzVTXTv3n3cuHGsbkI4IPeMmTNnDqvtz5gxQ19fn9VNCAf07xnT0tJib29fV1fHUvvXr18fMWIES40LDezvGWNoaDh9+nSWGnd0dBw2bBhLjQsQ5J5J7HV13nvvPbEY3izGQD+HSTKZzNnZuaysjPGW09LSBg0axHizggW7ECbp6OiEh4cz3qyXlxeEnlmQe4ax0dVh+0yRAEE/h3nu7u5Pnz5lsMG8vDwPDw8GGwSwv2fezJkzGWztrbfegtAzDnLPvHnz5jHYGnRy2AD9HFYMGDDg4cOHqrcjFouLioqcnJxUbwoQwf6eFUztpIcPHw6hZwPknhVz584ViUSqtwOdHJZAP4ctwcHBycnJqrSgr69fUlLSvXt3pkoCONjfs0X1XfX48eMh9CyB3LNl1qxZurq6qrQAnRz2QO7ZYmNjExoaSnt1Y2PjSZMmMVgPIILcs0iVHfbUqVONjY0ZLAYQQe5ZNH369G7dutFbFzo5rILcs8jU1HTixIk0VrSyshozZgzj9QAc5J5d9HbbM2fOhEtpWQXn79nV0tLi4OBQW1tLaa0bN27AVYWsgv09uwwNDadNm0ZplR49egwdOpSlegAGcs86ql2d2bNnw6W0bIN+DuuoXnSbnp7u5+fHakkA9iuso3TRrZeXF4SeA5B7Lijf1YHT9tyAfg5HlLzoFi6l5Qbs7zmizEW3gwcPhtBzA3LPEWUuuoVODmegn8OdgQMHZmVldfa/cCktl2B/z52ud+cjRoyA0HMGcs+d9957r4uLbqGTwyXo53Cqs4tu9fX1S0tLraysuC9JmGB/z6nOduoTJkyA0HMJcs+pzi66hU4OxyD3nOrwoltjY2O27wkHSCD3XFPctU+bNg0upeUY5J5rihfdQieHeypN8AI6I5PJamtr6+rqGhoaJBJJY2NjXV2dTCarr69HEMTb2zs9PR17prGxcWFh4e7du7t162ZoaGhkZGRiYmJiYmJhYYH9a2BgwOuvop3gPCZNKIqWlpYWFhYWFRUVFRW9fPmyrKysvLy8qqqqsrKyqqqKqRfW1NTU3t7exsbGxsbGzs7OycmpZ8+eLi4uLi4uzs7OcBkuPZB7pdTU1OTk5OTm5ubn5+fl5eXm5hYUFLS1tfFblVgs7tGjh4eHh6enp5eXl6enp6enZ48ePfitSiNA7jtWVFSUkZGRkZGRmZmZmZlZWFjId0XKsrKy8vPz8/2Ht7e3jo4O30WpJuQ5tQAAGVVJREFUHcj9/2pra0tLS0tJSUlOTk5JSSkpKVG9TVJnHeuTWFhYiESi8vLymzdvenp6DhgwAEGQ+vp6mUwml8tJhwSq12BqajpkyJCgoKDAwMDAwEBzc3PV29QCgs69TCa7f/9+QkJCQkJCcnJyS0sLpdXFYrGDgwPe23Z0dMS64Fhf3Nrauot5YbGLbs+fP9/1VYWvX7+urKzEDhiw4wfiEUVrayvVggcMGBAaGhoaGjps2DAhnzwVYu5LSkrOnTt34cKFxMRE5We2sbe39/b29vDw8PDwwBZcXFz09PRol7Fz587ly5fTXh07sM7Pz8cPOfLy8p4/fy6Xy5VZXV9f/+233x43blxYWBj2mSMoAsp9WlrauXPnzp49m56e/sbfWiQSeXh4+Pr6+vn5Yd1lW1tbZutBUZSRe6IQSSSSrKyszMxM7MgkKytLmYNvV1fXsLCwyZMnjxgxQiAniLQ/948fPz527Njhw4efPHnS9TONjY19fX39/f2HDh06cuRIa2trbipkj1QqffDgwe3bt9PS0m7evPnGo3MLC4tJkyaFh4ePHz9elY8y9ae1uS8oKDhw4EB8fHxubm4XTzMwMAgKCgoNDR09evRbb72l3ac+8vPzsYOZ69evV1dXd/FMa2vrGTNmREREBAUFcVYel7Qt983NzSdOnNi3b19iYmIXv5qbm1tYWNg777wTEhJCe6puzSWXyzMyMi5evHjmzJn79+93cUjg5eW1ePHiiIgIe3t7LitkHaotsrOzV6xY0cV5OrFYHBQUtHHjxsePH/NdrBopKyvbu3fvlClTuvj719XVnTJlyuXLl+VyOd/1MkPjcy+Tya5cuRIWFtbFMWLfvn2jo6OfPXvGd7Fqramp6cyZM+Hh4V0c2rq7u2/cuLGmpobvYlWlwblvamravn177969O3uT3Nzc1q1bB3Gnqrq6eu/evcHBwZ29sObm5p9//nlJSQnfldKnkbmvr6+PiYlxdHTs8F0xNDQMDw+/cuWK1nwo8yUvLy86OtrFxaXD11lfXz8iIiI3N5fvMunQsNzX1tZ+8803nXXiPTw8tm7dWldXx3eZWqW9vf3EiRMjR47s8DXX0dGZO3dufn4+32VSozG5b2xsjImJ6fDLI5FINHr06KNHj0qlUr7L1Ga5ubmRkZEdjm7Q1dWNiIgoKCjgu0ZlaUDu29vbd+zY4eDgoPhy6+npLViwIDs7m+8aBaSqqio6OrrD2R8MDQ0/++yz6upqvmt8M3XP/bVr1zocPWJgYBAREfHkyRO+CxSohoaGmJgYZ2dnxbfGysoqJiamvb2d7xq7or65f/r06dSpUxVfVn19/Y8++qisrIzvAgHa3Nz83//+t8POZ//+/RMSEvgusFPqmPv29vaYmBjFfqRYLA4PD3/69CnfBYJ/kUgkGzdutLCwUEx/eHh4eXk53wV2QO1yf/fu3Q47NmPHjoXvWdXZ69evIyMjFS856N69e1xcnLqdU1aj3Dc3N3/66aeKI8Pc3d3PnDnDd3VAKY8fPx47dqzibmvMmDFFRUV8V/d/1CX36enp/fr1I71YRkZGmzZtam1t5bs6QM3p06ddXV1J76aFhcWhQ4f4Lu1/8Z97uVweExOjOEvM8OHD8/Ly+K4O0NTY2BgVFaX46T1jxgxskhV+8Zz78vLyUaNGddgj5LcwwIjU1NSBAweS3l8XF5e7d+/yWxifub9165biGJsxY8a8evWKx6oAs9rb26Ojo0k7fl1d3Y0bN/JYFW+537JlC+lKNiMjox07dqjbgT9gxM2bN3v27Enax82ZM0cikfBSDw+5b21tXbRoEeklGDBggIaO7ANKqqurmzVrFul9HzRoUHFxMffFcJ37169fK47smzdvHl9/94Bju3btIl3X4ujoeP/+fY7L4DT3T58+dXd3J/7OhoaGu3fv5rIGwLuUlBTSJJ4mJiZnz57lsgbucp+dnU26T6W1tfXNmzc5KwCoj8rKyqFDhxLDoKOjExsby1kBHOX+/v37pOlofHx8nj9/zs3WgRpqaWl57733iJEQiUT//e9/udk6F7m/ceOGqakp8TccO3YsXBUF5HL56tWrSQd7mzZt4mDTrOc+JSWFFPopU6Y0NzezvV2gKbZv3y4W/+t+Uz/++CPbG2U39xkZGaQLc+bNm6fmVyQA7v3xxx/EgZwikWjHjh2sbpHF3D969Kh79+7E0H/00UfwtRTo0NGjR4nRF4vFf/zxB3ubYyv3paWlpBF5ixYtgtCDLhw7dow4nEFPT+/KlSssbYuV3Dc1Nb399tvE0EdERMhkMja2BbRJbGwssa9vZmaWlZXFxoaYz71MJpsyZQox9FOnToUZPoCStmzZQgxPr1692LhSkfncr1mzhli3v78/jEEAlHz00UfECI0YMYLxcyEM5/7q1avELpqrq2tpaSmzmwBaT7HLsHr1amY3wWTui4qKbGxs8FqNjY0fPnzIYPtAOCQSSf/+/YlnNpkdwPOv7wtUIZfL58+fX1lZif9k9+7dPj4+TLUPBMXY2Pj48eNmZmbYQxRFFy5cWFZWxtgGmPoDiomJITa7cuVKploGgnXq1CnibQ3CwsKYapmZ3Ofl5RkZGeH1+fv7wyQIgBGkY1ymxmwycH8rFEWHDRt2+/Zt7KGBgUFaWpripCAA0NDc3Ozn55eXl4c9NDc3z8nJ6XCSYEoY6N8fOHAADz2CIN999x2EHjClW7duhw4dwi/Frquri4qKYqBdFT8vamtriXe6GzJkCHxFBRhHzLpIJLp9+7aKDaqa+08//RQvSCwWc3+hJI/mzp2r/P5l4MCBb2yww1sqkAjzYp3GxkbipYl+fn4q7l5V6ucUFRXt2LEDf/jBBx/4+/ur0iAAHTIyMtq8eTP+MCMjIz4+XpUGVcr9+vXrW1tbsWUrK6v169er0hoAXZg5cyZxJo7vvvtOJpPRb472J8WLFy+IE0Js2LBBlc8dTffzzz8rvraXL1+m3eDKlSuxRtzc3ODyNExqairxdL4qk0nSz/2HH36IV2BjY9PQ0EC7KS0glUoVJ4J0d3dvaWmh0VpaWho+zOnChQuMV6u5wsLCiC8v7cHtNHNfXV1NPAj76aef6LWjTVJSUhTvmb527Vqq7chksoCAAGz18PBwNkrVXGlpacQX+dy5c/TaoZn7H3/8Ed+2hYUFjDTGLF26lJR7Q0NDqjcm2rlzJ7auqakpTJGraMKECfjLO27cOHqN0Mm9VCrt1asXvu1Vq1bR27b2qa6uJo5IxYwfP175FsrLyy0tLbEVOZtMRrP8/fff+GsrEolycnJoNEIn9xcvXsQ3LBaLnz17RqMRbbV//35EwfHjx5VcPSIiAlvF19cXvgHskFwu9/DwwF/bqKgoGo3Qyf3ixYvxrU6YMIFGC9pt+PDhpNw7Ozsrc9yfmJiI78bu3LnDQakaingu39XVlcZ8BZRz39raSpwS5+DBg1Rb0HrZ2dmkqf2V6Q22tbX17dsXe/KHH37ITakaqqSkhHhZX1JSEtUWKOf+zJkz+Pa6detWX19PtQUhUJz+TldXt+upATZu3Ig908bGRiNudc+vESNG4K9tZGQk1dUp53758uX49mbMmEF1dYFoampSvL1HcHBwZ5/IhYWF+AUMcG8vZfz222/4C9unTx+qq1POfZ8+ffDtwTvUhXPnziEK9u3b1+GTJ0+ejD1h+PDh3JapqYqLi4kvbEFBAaXVqeX+xYsXxI29fPmS0upCM23aNFLura2tX79+TXoa3nXU09ODe7Irz9vbG39h9+zZQ2ldauPSrl27hi/369fP2dmZ0upCs3XrVhMTE+JPqqqqvvzyS+JPmpubIyMjseXPP/8cP7QFbzRmzBh8mZhMZVDLfVpaGr6seJsqQNKjRw/SLFoIguzdu/fOnTv4w3Xr1mGfoj179vz66685rE7jERNITKZSKH06BAYG4it21lUFRO3t7cR5YDD4d1LEM54c3+BJCxQWFuIvqVgspnRqkULuZTIZ8VM7IyODeqlClJSUpDheLSYmBiWcjJs6dSrfZWok4s2jKF18SCH3z549w7ehr69Pb4StMC1ZsoSUe1NT002bNmHLxsbGhYWFfNeokUJDQ/GX9LffflN+RQr9+6KiInzZ1dXVwMBA+XUFbtOmTaTb2jU0NODXSkdHR7u4uPBRl8YjDtR5+fKl8itSyD2xXdL9R0HXrKysfvrppw7/y8fHh3htPqCEmEPifvmNaO7vYf9E1YIFC0JCQkg/FIlEO3fuJN7fBlBCzD1b+3vinK+qT1glNB1GfMSIEaTbFwNKiHcCr6ioUH5FCrlvamrCl0lfxwBl9OvXj3SjO+KkooAG4sWuxHy+Ec3cwxsG1AExh1zkvlu3bsqvCABLuMi9XC7/v9XEjN0wAgDaiFefUJpGikJ8iX9bzc3Nyq8IAEto970p5J7Yt4HcA3VAzL0ys+riaO7vGxsblV8RAJbQPuakkHvi5eTl5eXKrwgAS4h3eiOdI+4ahdzT/k4YAJYQc0hp7AzN3FP6ThgAltAeM0Yz94WFhcTTmgDw4vnz5/gypateKeTezc0NvzhIIpEQh+MDwIuMjAx8mXiZ+RtRyL2BgQGxaeImAeDe69evif0cxfsPdIHa165+fn74MuQe8CszMxNfdnJysrOzU35d+rm/desWpXUBYBYxgcRkKoNa7ocNG4Yv3717t76+ntLqQnP79m3Rv5G+9/j7779JT2hpaeGrWo1z5coVfJmYTGVQy72vry9+XwOpVHrjxg1KqwPAlIaGhtTUVPwhcQ4pZVDLvUgkIl7BfuHCBUqrA8CUK1eutLe3Y8s2NjYDBgygtDrl4cTjxo3Dl0+cOCGVSqm2IBxDhw6lOjGGoaEh31VrBuJ9m8eMGUN1YDzl3E+ZMgWfQaSiooLqvIQAqK6hoYE43fTMmTOptkA595aWlmPHjsUfHjlyhGoLAKjo9OnT+EhMCwuL8ePHU22BzmVTs2fPxpfj4+Orq6tpNAIAbbt27cKXp0+fTmMKMzq5nzJlirm5Obbc1NQUGxtLoxEA6MnMzLx9+zb+cP78+TQaoZN7Y2PjRYsW4Q+3bdtG6dJGAFSxbds2fLlfv35Uz9xjaF4evmLFCvwIurCw8K+//qLXDgCUlJSUHD58GH8YGRmpONe0Mmjm3t3dnXgwsXbtWhiWDDiwYcMG/CttS0vLuXPn0muH/nQgX331Fb78+PHjo0eP0m4KAGW8fPlyz549+MOPP/6Y0rXk/0L1ixUi4glNT0/PtrY2VVoDoGvE2whYWVnV1tbSbkql6Z/Wr1+P967y8vJ++eUXVVoDoAvp6enEM4erVq3CTyrSIEJRVJVqpkyZgt+G0szMLDc3F6ZKBoxDUXTo0KHJycnYQ3t7+ydPnqgyObGq0/1t2bIFH1JSX1//xRdfqNggAIoOHDiAhx5BkI0bN6o6I7fqvS7iAS6CIH/99ZfqbQKAKy4uJs7dFBgYKJfLVWxT1X4OgiBNTU3e3t74TCYODg4PHz6kNIkPAJ1BUXTixIn4iHexWHzv3j1/f38Vm2VgWmMjI6Pdu3fjB7ilpaUrV65UvVkAEATZu3cv8TKPzz77TPXQIwgT/RzM0qVLic3u3r2bqZaBYD18+JA4K6u3t3dzczMjLTPQz8E0Njb6+vo+ffoUe2hgYJCUlMTMnyYQJIlEEhAQkJOTgz3U1dVNTk4ePHgwI40zdvsGY2Pj2NhYfGKp1tbWmTNn1tTUMNU+EBQURRcvXoyHHkGQ7777jqnQ/+8GGLR582Zi48OHD4fbmgMa1qxZQwzSxIkTZTIZg+0znHu5XD5jxgxixQsXLmR2E0Dr/fnnn8RRlq6urlVVVcxuguHcoyhaW1vr5eVFjP53333H+FaAtrp+/bq+vj4eHiMjo7S0NMa3wnzuURQtKCggTtomEol+/fVXNjYEtExGRoalpSWeHLFYzNLXoKzkHkXR1NRU4hkokUgEZzZB17Kyskhfd8bExLC0LbZyj6Lo8ePHibdZ1NHROXz4MHubAxotOzvb1taWGPrIyEj2Nsdi7lEUjYuLI07oo6Ojs2fPHla3CDRRWloaKfTz589n9gQOCbu5R1H0999/Jx6bi0SizZs3s71RoEFu3rxJGkk/ffr09vZ2VjfKeu5RFP3555+Rf/v6669VH1IHtMDZs2dJ91ueMmUKBxfucZF7FEV37txJmsEwPDy8qamJm60D9bRr1y5dXV1iKubMmcPN1aoc5R5F0T///BMfxYB5++23y8rKOCsAqA+pVBoZGUnqBSxfvpzVPj0Rd7lHO/pQ69WrV3p6Opc1AN5VVVURZ9XGfPPNN1zWwGnuURTNzMwk3WfUwMCAvdO0QN3cv3+/V69exADo6uru3LmT4zK4zj2Koi9fvvT19SX9uS9cuBC6+1pv+/btxDEICIJYWVldv36d+0p4yD2Kog0NDdOmTSNFv2/fvmyMxADqoKKiYurUqaR33NvbOy8vj5d6+Mk9iqJyuTwmJoZ0pKurqxsdHS2VSvmqCrDh8uXLjo6OpNBPmzZNlYmfVMRb7jE3btxQnG9n6NChfO0GALPq6uqWLVtGmrpVX1//l19+4bcwnnOPomhZWdk777xDir6hoeG6detg4kGN9tdffzk5OZHeWXd397t37/JdmhrkHkVRuVy+Y8cO0ilOBEF8fHySkpL4rg5Q9vLlS8XePIIgS5culUgkfFeHomqSe0xubq7iBZQikWjevHmvXr3iuzqglKampnXr1ilOU2xra3v69Gm+q/s/apR7FEVlMtmuXbtMTU1Jr5qRkVF0dDSc6FRzZ86cIZ2bx4SHh1dWVvJd3b+oV+4xz58/nzBhguLL5+Li8vvvv7M9Ug/QkJiYGBwcrPiWubu7X7t2je/qOqCOucccOXKE9M0uxtPTMz4+HoZzqonU1FTFQQfYR/SaNWuYmuaJceqbexRFGxsbo6OjFY93EQTx9fWNj4/nbBgTUHT37t0pU6Yo3l5KJBLNnj27qKiI7wK7ota5xxQVFb333nsd3ojdw8Nj7969ra2tfNcoLAkJCaGhoYpvB4IgAQEBt2/f5rvAN9OA3GMyMzMnTpzY4Wvt7Oy8YcMGdTty0j6tra0HDx7sbNKyfv36/fXXX5rS/9SY3GNu3749fPjwDl93Q0PDxYsXw6hmNhQXF3/77bf29vYdvvK9e/c+cOCAZvU5NSz3mJs3b06YMKGzG5cGBgbu2bOnvr6e7zI1nlQqPXfu3PTp00nDqIj7+D/++EMTz7BpZO4xGRkZs2bNIk5VQmRsbLxgwYIbN25oyievWsnLy1u9erXiYDLckCFDTp06pbmvrQbnHlNcXBwdHd3F7VWcnZ0jIyNv3bqluW8SZ4qKimJiYoKDgzv7LP3/7d3BS/JgHAfw0CLFISOadlhTBB2ZuRJKl3Xy2oJO3oQu/QnRpT+hf6BT18AK6lKEEgqbFDWLQsQonUTlIrKmlVN5DwN5kVq9r5Xmns/B0/PoM/jO5/fA9jxqtXpqamp3d7fZI23Ur8+9pFAoLC8vDw0NvZf+jo4Oi8WysLBA0/TvqkR/QCqVWlpaIklS5sx7o9G4uLh4dXXV7MF+jTbJfU0sFpubm9Pr9TI3gMFgmJ2dXV9fb5FnpJqiXC5Ho9H5+fm6TXzrdHZ2UhS1sbHRZs/Gftl5Jy2lWCwGg8GVlZVIJFKpVN5r1tXV5fF4fD6fz+dzu93vrd7aydnZWTgcDoVCe3t7+XxepqXdbg8EAoFAoC0PJG7P3NdcX18Hg8HV1VWapuWvFIIgr9dLkiRJkh6PR37G+EVEUTw6OmIYhmGYSCRyc3Mj395qtfr9fr/f73A4fmaETdHmua/JZrNra2tbW1vRaFQURfnGKpVqcHDQ7XaPjIwMDw87nc5GTwn+QeVyOZFIxONxlmUPDg4ODw+fn58/7EUQBEVRMzMzLpfrBwbZdErJfc3Dw8P29vbm5ubOzs79/f1nuqhUKqvVShAEjuMDAwM4jttstha5E0RRvLi4SCQSyWQymUyenJycnp6+vr5+pq9Go5mcnJyenqYoymQyffdQW4ricl9TrVZZlg2FQuFwOBqNFovFf+qOoqjZbDabzRiG9ff3YxiGoiiCIL29vd+xTuB5nuf529tbjuPS6XQ2m+U4LpPJXF5efjh9/U2tVrtcLmlJ4/V6tVrtlw/1V1Bu7v9WKpX29/dpmqZpmmGYXC7XyLf19PQYDAYEQSAIgiAIhmEIgnQ6nTRFqNXqusVDsViU/qFfXl4KhUI+n396ehIEQRCEu7s7KfEyq/MP6XS60dHR8fFxkiQnJiZgGG7k6toDyP0bzs/PY7EYy7LHx8csy36yHGodWq3W4XBIi5OxsTGCIOq2XwVA7j/GcVw8HpdqaOmzpc7l1Wg0NpsNx3Ecx+12u9PpxHEcBF0eyP3/yOVyqVQqk8lwHCeV2ul0WipIqtXqN/0oDMNGoxFFUQzDMAwzmUwYhlksFpPJ9ObLCYAMkPuvVK1WaxU5z/NSmS6V7I+Pj5VKRRRFQRCkxqVSqbZZZHd3t/RaGQzD0kpAWhjo9fq+vj4EQRAEqdtZEmgEyD2gRGB+BJQI5B5QIpB7QIlA7gElArkHlAjkHlAikHtAiUDuASUCuQeUCOQeUCKQe0CJQO4BJQK5B5ToD3ZbA2LRNlT3AAAAAElFTkSuQmCC\n",
      "text/plain": "<IPython.core.display.Image object>"
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\nResult for identification using ID Algorithm:\nSum over {X1}:\n\tPredictor: P(X1|T)\n\tPredictor: P(Y|T,X1)\n"
     ]
    }
   ],
   "source": [
    "# Random data\n",
    "treatment = \"T\"\n",
    "outcome = \"Y\"\n",
    "variables = [\"X1\"]\n",
    "causal_graph = \"digraph{T->X1;X1->Y;}\"\n",
    "columns = list(treatment) + list(outcome) + list(variables)\n",
    "df = pd.DataFrame(columns=columns)\n",
    "\n",
    "# Causal Model Initialization\n",
    "causal_model = CausalModel(df, treatment, outcome, graph=causal_graph)\n",
    "\n",
    "# View graph\n",
    "causal_model.view_model()\n",
    "from IPython.display import Image, display\n",
    "print(\"Graph:\")\n",
    "display(Image(filename=\"causal_model.png\"))\n",
    "\n",
    "# Causal Identification using the ID Algorithm\n",
    "identified_estimand = causal_model.identify_effect(method_name=\"id-algorithm\")\n",
    "print(\"\\nResult for identification using ID Algorithm:\")\n",
    "print(identified_estimand)\n"
   ]
  },
  {
   "source": [
    "## Case 4\n",
    "\n",
    "The example exhibits the performance of the algorithm in the presence of a direct and indirect path(through **X1**) from **T** to **Y**."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Graph:\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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\n",
      "text/plain": "<IPython.core.display.Image object>"
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\nResult for identification using ID Algorithm:\nSum over {X1}:\n\tPredictor: P(Y|T,X1)\n\tPredictor: P(X1|T)\n"
     ]
    }
   ],
   "source": [
    "# Random data\n",
    "treatment = \"T\"\n",
    "outcome = \"Y\"\n",
    "variables = [\"X1\"]\n",
    "causal_graph = \"digraph{T->Y;T->X1;X1->Y;}\"\n",
    "columns = list(treatment) + list(outcome) + list(variables)\n",
    "df = pd.DataFrame(columns=columns)\n",
    "\n",
    "# Causal Model Initialization\n",
    "causal_model = CausalModel(df, treatment, outcome, graph=causal_graph)\n",
    "\n",
    "# View graph\n",
    "causal_model.view_model()\n",
    "from IPython.display import Image, display\n",
    "print(\"Graph:\")\n",
    "display(Image(filename=\"causal_model.png\"))\n",
    "\n",
    "# Causal Identification using the ID Algorithm\n",
    "identified_estimand = causal_model.identify_effect(method_name=\"id-algorithm\")\n",
    "print(\"\\nResult for identification using ID Algorithm:\")\n",
    "print(identified_estimand)\n"
   ]
  },
  {
   "source": [
    "# Case 5\n",
    "\n",
    "This example exhibits the performance of the algorithm in the presence of a confounding variable(**X1**) and an instrumental variable(**X2**)."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Graph:\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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\n",
      "text/plain": "<IPython.core.display.Image object>"
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\nResult for identification using ID Algorithm:\nSum over {X1}:\n\tPredictor: P(Y|X2,X1,T)\n\tPredictor: P(X1)\n"
     ]
    }
   ],
   "source": [
    "# Random data\n",
    "treatment = \"T\"\n",
    "outcome = \"Y\"\n",
    "variables = [\"X1\", \"X2\"]\n",
    "causal_graph = \"digraph{T->Y;X1->T;X1->Y;X2->T;}\"\n",
    "columns = list(treatment) + list(outcome) + list(variables)\n",
    "df = pd.DataFrame(columns=columns)\n",
    "\n",
    "# Causal Model Initialization\n",
    "causal_model = CausalModel(df, treatment, outcome, graph=causal_graph)\n",
    "\n",
    "# View graph\n",
    "causal_model.view_model()\n",
    "from IPython.display import Image, display\n",
    "print(\"Graph:\")\n",
    "display(Image(filename=\"causal_model.png\"))\n",
    "\n",
    "# Causal Identification using the ID Algorithm\n",
    "identified_estimand = causal_model.identify_effect(method_name=\"id-algorithm\")\n",
    "print(\"\\nResult for identification using ID Algorithm:\")\n",
    "print(identified_estimand)\n"
   ]
  },
  {
   "source": [
    "## Case 6\n",
    "\n",
    "This example exhibits the performance of the algorithm in case of a disjoint graph."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Graph:\n"
     ]
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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\n",
      "text/plain": "<IPython.core.display.Image object>"
     },
     "metadata": {}
    },
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "\nResult for identification using ID Algorithm:\nSum over {X1}:\n\tPredictor: P(X1,Y)\n"
     ]
    }
   ],
   "source": [
    "# Random data\n",
    "treatment = \"T\"\n",
    "outcome = \"Y\"\n",
    "variables = [\"X1\"]\n",
    "causal_graph = \"digraph{T;X1->Y;}\"\n",
    "columns = list(treatment) + list(outcome) + list(variables)\n",
    "df = pd.DataFrame(columns=columns)\n",
    "\n",
    "# Causal Model Initialization\n",
    "causal_model = CausalModel(df, treatment, outcome, graph=causal_graph)\n",
    "\n",
    "# View graph\n",
    "causal_model.view_model()\n",
    "from IPython.display import Image, display\n",
    "print(\"Graph:\")\n",
    "display(Image(filename=\"causal_model.png\"))\n",
    "\n",
    "# Causal Identification using the ID Algorithm\n",
    "identified_estimand = causal_model.identify_effect(method_name=\"id-algorithm\")\n",
    "print(\"\\nResult for identification using ID Algorithm:\")\n",
    "print(identified_estimand)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}